Preheat oven to 450°. Transfer chicken and marinade to a foil-lined rimmed baking sheet, placing chicken skin side down. Roast until fat begins to render, 15–20 minutes. Turn chicken skin side up and continue to roast, basting occasionally with pan drippings, until chicken is cooked through and deeply browned, 15–20 minutes longer.

After turning chicken, toss asparagus and scallions with oil on another rimmed baking sheet; season with salt and pepper. Roast, shaking pan halfway through, until tender, 10–15 minutes (thinner stalks will cook more quickly).

Transfer chicken to a platter. Pour any pan juices into a glass measuring cup. Let sit a few minutes, then spoon off fat from surface.